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Prove that the greatest integer function...

Prove that the greatest integer function `f : R rarrR` given by `f(x) =[x]` is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  5. Discuss the continuity of sine function.

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  9. Examine the following functions for continuity f(x)=1/(x-5)

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  10. Prove that the function f(x)=x^n is continuous at x=n, where n is a p...

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  11. Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continu...

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  12. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

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  13. Find all points of discontinuity of f, where f is defined by f(x)={(|...

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  14. Evalute lim(xrarr0)f(x) , where f(x)={(absx/x, x ne 0),(0,x=0):}

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  15. Find all points of discontinuity of f, where f is defined by f(x)={(x/...

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  16. Examine the continuity of the function <be> f(x)={(x+1,xge1),(x^2+1,x<...

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  17. Examine the continuity of the function f(x)={(x^3-3, if ,x le 2),...

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  18. Examine whether the function defined by f(x)={(x+5,xle1),(x-5,x>1):}...

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  19. Discuss the continuity of the function f(x)={(2 x , if , xlt0),( 0,...

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  20. Find the derivative of the function given by f(x)=sin (x^2)

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